Counterexamples to Proposed Dollar-Unit Sampling Algorithm
针对Menzefricke提出的美元单位抽样算法，通过反例证明其关于第二种停止规则的猜想是错误的，对审计和抽样领域的研究者有参考价值。
In a recent article, Menzefricke [1983] adapted the fixed constrained optimization approach (Boockholdt and Finley [1980]) to dollar-unit sampling. In Menzefricke's model, the auditor's objective is to determine the n, k pair (sample size and acceptance number) that minimizes total expected costs subject to a type II risk constraint. He provided an algorithm for determining the optimal n, k pair with two possible stopping rules, one which he proved would be optimal and one which he conjectured would also lead to an optimal solution. In this note I provide some counterexamples that demonstrate that his conjecture about the second stopping rule was incorrect.